Question

consider the figure shown. assume that the vertical lines intersect the horizontal lines at right angles. there are select choice pairs of parallel lines. there are select choice pairs of perpendicular lines.

Explanation:

Step1: Count parallel - horizontal lines

There are 3 horizontal lines. The number of pairs of parallel - horizontal lines is calculated using the combination formula $C(n,2)=\frac{n(n - 1)}{2}$, where $n = 3$. So, $C(3,2)=\frac{3\times(3 - 1)}{2}=\frac{3\times2}{2}=3$.

Step2: Count parallel - vertical lines

There are 3 vertical lines. Using the combination formula $C(n,2)$ with $n = 3$, we get $C(3,2)=\frac{3\times(3 - 1)}{2}=3$.

Step3: Total number of parallel - line pairs

The total number of pairs of parallel lines is the sum of parallel - horizontal and parallel - vertical pairs, $3+3 = 6$.

Step4: Count perpendicular - line pairs

Each horizontal line intersects each vertical line at a right - angle. Each of the 3 horizontal lines forms 3 perpendicular pairs with the 3 vertical lines. So the number of pairs of perpendicular lines is $3\times3=9$.

Answer:

There are 6 pairs of parallel lines.
There are 9 pairs of perpendicular lines.